A hot-air balloon with an inflated diameter of 30 ft is carrying a weight of 800 lb, which includes the weight of the hot air inside the balloon. Assume that the variation of density in the standard atmosphere is given by p= 0.002377[1 0.000007h]4.21, where h is the altitude in feet and p is in slug/ft. a) Calculate balloon's upward acceleration at sea level the instant the restraining ropes are released. (7 points) b) Calculate the maximum altitude the balloon can achieve. (3 points)